What is the integral of cos(8x)cos(5x) ?

The integral of cos(8x)cos(5x) is 1/2 (1/13 sin(13x)+1/3 sin(3x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(8x)cos(5x)

\int cos (8 x) cos (5 x) d x

\frac{1}{2} (\frac{1}{13} sin (13 x) + \frac{1}{3} sin (3 x)) + C

Solution steps

\int cos (8 x) cos (5 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (cos (13 x) + cos (3 x)) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int cos (13 x) + cos (3 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int cos (13 x) d x + \int cos (3 x) d x)

\int cos (13 x) d x = \frac{1}{13} sin (13 x)

\int cos (3 x) d x = \frac{1}{3} sin (3 x)

= \frac{1}{2} (\frac{1}{13} sin (13 x) + \frac{1}{3} sin (3 x))

Add a constant to the solution

= \frac{1}{2} (\frac{1}{13} sin (13 x) + \frac{1}{3} sin (3 x)) + C

\frac{d}{d x} (\frac{5 x}{3})

\frac{9 s}{9 s ^{2} + 1}

\frac{e ^{- s}}{s ^{5}}

x \to 0 lim (\frac{( 4 ^{x} - 1 )}{x})

What is the integral of cos(8x)cos(5x) ?
The integral of cos(8x)cos(5x) is 1/2 (1/13 sin(13x)+1/3 sin(3x))+C